Question

Given that f(x) = x sqaured - 10x + 16 and g(x) = x - 8, find f (x) · g(x) andexpress the result in standard form.

Answer 1

Given the functions

`f(x)=x^2-10x+16`
`g(x)=x-8`

You have to calculate

`f(x)\cdot g(x)`
`(x^2-10x+16)\cdot(x-8)`

To solve this you have to apply the distributive property of multiplications, that is, you have to multiply each term of the first parenthesis with each term of the second parenthesis.

As follows:

`\begin{gathered} (x^2-10x+16)\cdot(x-8) \\ (x^2\cdot x)+(x^2)\cdot(-8)+(-10x\cdot x)+(-10x)\cdot(-8)+(16\cdot x)+(16\cdot(-8)) \\ x^3-8x^2-10x^2+80x+16x-128 \end{gathered}`

Now simplify the like terms

`\begin{gathered} x^3+(-8x^2-10x^2)+(80x+16x)-128 \\ x^3-18x^2+96x-128 \end{gathered}`

The result in standard form is

`f(x)\cdot g(x)=x^3-18x^2+96x-128`